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Neural Computation

March 1, 1997, Vol. 9, No. 3, Pages 623-635
(doi: 10.1162/neco.1997.9.3.623)
© 1997 Massachusetts Institute of Technology
Hyperparameter Selection for Self-Organizing Maps
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The self-organizing map (SOM) algorithm for finite data is derived as an approximate maximum a posteriori estimation algorithm for a gaussian mixture model with a gaussian smoothing prior, which is equivalent to a generalized deformable model (GDM). For this model, objective criteria for selecting hyperparameters are obtained on the basis of empirical Bayesian estimation and cross-validation, which are representative model selection methods. The properties of these criteria are compared by simulation experiments. These experiments show that the cross-validation methods favor more complex structures than the expected log likelihood supports, which is a measure of compatibility between a model and data distribution. On the other hand, the empirical Bayesian methods have the opposite bias.